Is it possible to render a panorama in perspectives other than full 360°x180°?
This is not a very efficient way of doing this because it requires rendering the entire $360^\circ \times 180^\circ$ image and then cropping off a good chunk of it, but it seems to be the only option.

Here is a diagram:



$H$ is the height of the $360^\circ \times 180^\circ$ image, $h$ is the height of the cropped ($360°\times n^\circ$) image, and $n$ is the desired angle.  When $n$ is $180^\circ$ we can see that $D$ would be $\frac{1}{2}$ the height of the image so $D=\frac{H}{2}$.  From here it is just a little simple trigonometry and we can get:

$$
h = \sin(\frac{n}{2})\frac{H}{2}2 = \sin(\frac{n}{2})H
$$

Using your example of $30^\circ$ we get $h = \sin(15) H ≈ 0.26 H$  A slight rearrangement gives $H ≈ \frac{h}{0.26}$ which you can use to plug in the desired height and get the height you must use to render.